It is currently 18 Nov 2017, 03:48

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If m and k are integers, is x an integer?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 396

Kudos [?]: 348 [0], given: 10

Location: India
GMAT 1: 760 Q50 V44
If m and k are integers, is x an integer? [#permalink]

Show Tags

New post 23 Feb 2016, 18:34
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

51% (01:20) correct 49% (01:31) wrong based on 89 sessions

HideShow timer Statistics

If \(m\) and \(k\) are integers, and \(x^m = k\), is \(x\) an integer?

(1) \(-1 < k <2\)
(2) \(m > 0\)
[Reveal] Spoiler: OA

_________________

Reach out to us at bondwithus@gmatify.com

Image

Kudos [?]: 348 [0], given: 10

Expert Post
3 KUDOS received
Math Expert
User avatar
P
Joined: 02 Aug 2009
Posts: 5201

Kudos [?]: 5825 [3], given: 117

If m and k are integers, is x an integer? [#permalink]

Show Tags

New post 24 Feb 2016, 03:49
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
TeamGMATIFY wrote:
If \(m\) and \(k\) are integers, and \(x^m = k\), is \(x\) an integer?

(1) \(-1 < k <2\)
(2) \(m > 0\)



hi,

\(x^m = k\), m and k are integers, is x an integer..

(1) \(-1 < k <2\)
since k is an integer, k=0 or 1..
so
1) x^m=0
here x will be 0 as m is an integer
or x^m=1..
here it is possible x is a fraction or non integer while m=0, and x is an integer 1, with m as any integer..
insuff

(2) \(m > 0\)
m can be any integer greater than 0, but we do not know anything about k..
m acn be 2 and x \(\sqrt{3}\), then k will be an integer..
or m=2 and x =3 , here k will again be an integer..
so x can be a non integer or integer..
insuff.

combined..
we know m>0, so x^m=1, only when x is 1..
Suff..

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5825 [3], given: 117

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4314

Kudos [?]: 3034 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
Re: If m and k are integers, is x an integer? [#permalink]

Show Tags

New post 24 Feb 2016, 22:31
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If m and k are integers, and x^m=k , is x an integer?

(1) −1<k<2
(2) m>0


In the original condition, there are 3 variables(x,k,m) and 1 equation(x^m=k), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), if k is an integer not x, k=0,1, which only satisfies 1^m=1, 0^m=0. So, it is yes and sufficient.
Thus, C is the answer.


 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3034 [0], given: 0

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15697

Kudos [?]: 281 [0], given: 0

Premium Member
Re: If m and k are integers, is x an integer? [#permalink]

Show Tags

New post 21 Oct 2017, 13:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 281 [0], given: 0

Re: If m and k are integers, is x an integer?   [#permalink] 21 Oct 2017, 13:45
Display posts from previous: Sort by

If m and k are integers, is x an integer?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.